Reliability estimation of a complex renewable system with an unbounded number of repair units

In this study an asymptotical analysis of the reliability of a complex renewable system with an unbounded number of repair units is provided. The system state is given by a binary vector e(t)=[e1(t),...,en(t)], ei(t)=0(1), if at moment t the ith element is failure-free (failed). The authors assume that at the state e the ith element has failure intensity λi(e). At the instant of failure of every element the renewal work begins and the renewal time has distribution function Gi(t). Let EÅ- be the set of failed system states. The goal of this study is the asymptotic estimation of the distribution of the time until the first system failure, τ=inf{t:e(t)∈EÅ-∈e(0)=ℝn0∈.